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# Texas Assessment of Math Knowledge and Skills-Answer Key

Objective 6:

The student will demonstrate an understanding of geometric relationships and
spatial reasoning.

G(b)(4) Geometric structure. The student uses a variety of representations to describe geometric
relationships and solve problems .

(A) The student selects an appropriate representation ([concrete,] pictorial, graphical, verbal, or
symbolic ) in order to solve problems.

G(c)(1)Geometric patterns. The student identifies, analyzes, and describes patterns that emerge from
two- and three-dimensional geometric figures.

(A) The student uses numeric and geometric patterns to make generalizations about geometric
properties, including properties of polygons , ratios in similar figures and solids, and angle
relationships in polygons and circles.

(B) The student uses the properties of transformations and their compositions to make
connections between mathematics and the real world in applications such as tessellations
or fractals.

(C) The student identifies and applies patterns from right triangles to solve problems, including
special right triangles (45-45-90 and 30-60-90) and triangles whose sides are Pythagorean
triples.

G(e)(3) Congruence and the geometry of size. The student applies the concept of congruence to
justify properties of figures and solve problems.

(A) The student uses congruence transformations to make conjectures and justify properties of
geometric figures.

Objective 7:

The student will demonstrate an understanding of two - and three-dimensional
representations of geometric relationships and shapes.

G(d)(1) Dimensionality and the geometry of location. The student analyzes the relationship between
three-dimensional objects and related two-dimensional representations and uses these
representations to solve problems.

(B) The student uses nets to represent [and construct] three-dimensional objects.

(C) The student uses top, front, side, and corner views of three-dimensional objects to create
accurate and complete representations and solve problems.

G(d)(2) Dimensionality and the geometry of location. The student understands that coordinate
systems provide convenient and efficient ways of representing geometric figures and uses them
accordingly.

(A) The student uses one- and two-dimensional coordinate systems to represent points, lines,
line segments , and figures.

(B) The student uses slopes and equations of lines to investigate geometric relationships,
including parallel lines, perpendicular lines, and [special segments of] triangles and other
polygons.

(C) The student [develops and] uses formulas including distance and midpoint.

G(e)(2) Congruence and the geometry of size. The student analyzes properties and describes
relationships in geometric figures.

(D) The student analyzes the characteristics of three-dimensional figures and their component
parts.

Objective 8:

The student will demonstrate an understanding of the concepts and uses of
measurement and similarity.

G(e)(1) Congruence and the geometry of size. The student extends measurement concepts to find
area, perimeter, and volume in problem situations.

(A) The student finds area of polygons and composite figures.

(B) The student finds areas of sectors and arc lengths of circles using proportional reasoning .

(C) The student [develops, extends and] uses the Pythagorean Theorem.

(D) The student finds surface area and volumes of prisms, pyramids, spheres, cones, and
cylinders in problem situations.

G(f)(1) Similarity and the geometry of shape. The student applies the concepts of similarity to justify
properties of figures and solve problems.

(A) The student uses similarity properties and transformations to [explore and] justify conjectures

(B) The student uses ratios to solve problems involving similar figures.

(C) In a variety of ways, the student [develops,] applies, and justifies triangle similarity
relationships, such as right triangle ratios, [ trigonometric ratios ,] and Pythagorean triples.

(D) The student describes the effect on perimeter, area, and volume when length, width, or
height of a three-dimensional solid is changed and applies this idea in solving problems.

Objective 9:

The student will demonstrate an understanding of percents, proportional
relationships, probability, and statistics in application problems.

(8.3) Patterns, relationships, and algebraic thinking. The student identifies proportional relationships
in problem situations and solves problems. The student is expected to

(B) estimate and find solutions to application problems involving percents and proportional
relationships such as similarity and rates.

(8.11) Probability and statistics. The student applies the concepts of theoretical and experimental
probability to make predictions. The student is expected to

(A) find the probabilities of compound events (dependent and independent); and

(B) use theoretical probabilities and experimental results to make predictions and decisions .

(8.12) Probability and statistics. The student uses statistical procedures to describe data. The
student is expected to

(A) select the appropriate measure of central tendency to describe a set of data for a particular
purpose; and

(C) construct circle graphs, bar graphs, and histograms, with and without technology.

(8.13) Probability and statistics. The student evaluates predictions and conclusions based on
statistical data. The student is expected to

(B) recognize misuses of graphical or numerical information and evaluate predictions and
conclusions based on data analysis.

Objective 10:

The student will demonstrate an understanding of the mathematical processes
and tools used in problem solving.

(8.14) Underlying processes and mathematical tools. The student applies Grade 8 mathematics to
solve problems connected to everyday experiences, investigations in other disciplines, and activities
in and outside of school. The student is expected to

(A) identify and apply mathematics to everyday experiences, to activities in and outside of school,
with other disciplines, and with other mathematical topics;

(B) use a problem-solving model that incorporates understanding the problem, making a plan,
carrying out the plan, and evaluating the solution for reasonableness; and

(C) select or develop an appropriate problem-solving strategy from a variety of different types ,
including drawing a picture , looking for a pattern, systematic guessing and checking, acting
it out, making a table, working a simpler problem , or working backwards to solve a problem.

(8.15)  Underlying processes and mathematical tools. The student communicates about Grade 8

mathematics through informal and mathematical language, representations, and models. The
student is expected to

(A) communicate mathematical ideas using language, efficient tools, appropriate units, and
graphical, numerical, physical, or algebraic mathematical models.

(8.16)  Underlying processes and mathematical tools. The student uses logical reasoning to make

conjectures and verify conclusions. The student is expected to

(A) make conjectures from patterns or sets of examples and nonexamples; and

(B) validate his/her conclusions using mathematical properties and relationships.

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